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This self-contained guide introduces two pillars of data science, probability theory, and statistics, side by side, in order to illuminate the connections between statistical techniques and the probabilistic concepts they are based on. The topics covered in the book include random variables, nonparametric and parametric models, correlation, estimation of population parameters, hypothesis testing, principal component analysis, and both linear and nonlinear methods for regression and classification. Examples throughout the book draw from real-world datasets to demonstrate concepts in practice and confront readers with fundamental challenges in data science, such as overfitting, the curse of dimensionality, and causal inference. Code in Python reproducing these examples is available on the book's website, along with videos, slides, and solutions to exercises. This accessible book is ideal for undergraduate and graduate students, data science practitioners, and others interested in the theoretical concepts underlying data science methods.
Tensors are essential in modern day computational and data sciences. This book explores the foundations of tensor decompositions, a data analysis methodology that is ubiquitous in machine learning, signal processing, chemometrics, neuroscience, quantum computing, financial analysis, social science, business market analysis, image processing, and much more. In this self-contained mathematical, algorithmic, and computational treatment of tensor decomposition, the book emphasizes examples using real-world downloadable open-source datasets to ground the abstract concepts. Methodologies for 3-way tensors (the simplest notation) are presented before generalizing to d-way tensors (the most general but complex notation), making the book accessible to advanced undergraduate and graduate students in mathematics, computer science, statistics, engineering, and physical and life sciences. Additionally, extensive background materials in linear algebra, optimization, probability, and statistics are included as appendices.
This chapter examines the critical role of evaluation within the framework of recommender systems, highlighting its significance alongside system construction. We identify three key aspects of evaluation: the impact of metrics on optimization quality, the collaborative nature of evaluation efforts across teams, and the alignment of chosen metrics with organizational goals. Our discussion spans a comprehensive range of evaluation techniques, from offline methods to online experiments. We explore offline evaluation methods and metrics, offline simulation through replay, online A/B testing, and fast online evaluation via interleaving. Ultimately, we propose a multilayer evaluation architecture that integrates these diverse methods to enhance the scientific rigor and efficiency of recommender system assessments.
The introduction of advanced deep learning models such as Microsoft’s Deep Crossing, Google’s Wide&Deep, and others like FNN and PNN in 2016 marked a significant shift in the field of recommender systems and computational advertising, establishing deep learning as the dominant approach. This chapter discusses the evolution of traditional recommendation models and highlights two main advancements in deep learning models: enhanced expressivity for uncovering hidden data patterns and flexible model structures tailored to specific business use cases. Drawing on techniques from computer vision, speech, and natural language processing, deep learning recommendation models have rapidly evolved. The chapter summarizes several influential deep learning models and constructs an evolution map. These models are selected based on their industry impact and their role in advancing deep learning recommender systems. Additionally, the chapter will introduce applications of Large Language Models (LLMs) in recommender systems, exploring how these models further enhance recommendation technologies.